Mmellanea 
101 
Lastly, turning to the still-born rate, we have for the parabola of the fourth order a mean 
error of "051 and for the straight line a mean error of -075, corresponding to 2'5 and 3-7 per- 
centage errors respectively. This is a sensible betterment, but nothing like as good as in the case 
of the population data. We may say that by using a high parabola instead of a straight line we 
better the tit two-and-a-half times for the population, one-and-a-half times for the still-born, and 
one-and-a-quarter times for the death-rate. In the last two cases therefore straight lines would 
give quite reasonable graduation or interpolation formulae. 
The actual equations to the ctu'vcs, tlie year 1894 being in each ease taken as origin of r, the 
unit of which is a year, are ; 
Population. Straight line : 
?/ = 639-1007 -I- 29-81 86.f. 
Fifth order parabola : 
y = 617-729-|-44-8543.v-t-3-599,110.r2- l-555,483.»- - -083,91 7.'''H-033,424.p'. 
The unit of y is here 1000 individuals. 
Death-rate per 1000. Straight line : 
?/ = 22-5383 -l-0428.f. 
Fourth order parabola : 
j/ = 21-9981 - l-345,685.r-f- -052,220.r2 + -014,016.r3- -000,330.f''. 
The unit of y is one in the thousand. 
Still-horn per 1000. Straight line : 
j/ = 2-0471 --08799.t'. 
Fourth order parabola : 
3/ = 2-0173- -130,823.1 + -005,310.1- -f- -001,983,r'- -000,I31,r'. 
The unit of y is one in the thousand. 
The results obtained l)y observation and from calculation by the parabolas between the years 
1888 and 1900 are given in the accompanying Table II. This table shows at once that the 
results are quite satisfactory within the range of observation. The same point is brought out 
graphically from the diagram. Confining our attention to the curves between the verticals I'j I', 
and YoY.^, we could hardly hope to better the graduation provided. 
TABLE II. 
Interpolation Calculations. 
Population in lOOO's 
Death-Bate per 1000 i 
Still-born Rate per 1000 
Year 

Calculated 
Difference 
Calculated 
Difference | 
Calculated 
Difference 
1888 
446 
- 9 
28-50 
+ 1-33 
2-40 
--05 
1889 
521 
28-08 
- -07 ! 
2-47 
-•02 
1890 
540 
27-24 
-2-76 
2-47 
+ •11 
1891 
543 
+ 8 
26-10 
+ 1-78 
2-39 
--07 
1892 
552 
- 3 
24-78 
+ -73 i 
2-28 
-•01 
1893 
578 
_ -2 
23-38 
+ -98 
215 
-■07 
1894 
189r> 
618 
+ 15 
22-00 
- -72 
2-02 
-•04 
605 
-13 
20-72 
-1-28 
1-89 
+ •10 
1890 
709 
- 3 
19-62 
+ -46 
1-79 
-(-•01 
1897 
744 
+ 6 
18-78 
- -47 
1-72 
-■06 
189S 
768 
-f 2 
18-26 
+ -59 
1-67 
-03 
1899 
790 
— 5 
18-12 
+ 1-06 
1-66 
-f-03 
1900 
831 
+ 10 
18-40 
-1-69 
1-68 
•00 
